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The hardware-circuit-realized adaptive method (HCAM) and neuron-based adaptive algorithm (NAA) are two typical adaptive detection methods for harmonic and reactive currents. HCAM and NAA have the same detection principle (adaptive noise-canceling technology and a strong adaptive ability). In this letter, the algorithm of HCAM is obtained according to its detection circuit, whereas the simplest NAA is derived from a NAA. A comparison of the algorithm of HCAM with the simplest NAA shows that they are the same. This is the consistency between HCAM and NAA. The accuracy of this consistency is validated by simulation and experimental results.